A369708 Maximal coefficient of (1 + x^3) * (1 + x^5) * (1 + x^7) * ... * (1 + x^prime(n)).

1, 1, 1, 1, 1, 1, 2, 2, 4, 5, 8, 14, 23, 40, 70, 126, 221, 394, 711, 1290, 2354, 4344, 8015, 14868, 27585, 51094, 95160, 178436, 335645, 634568, 1202236, 2261052, 4267640, 8067296, 15318171, 29031484, 55248527, 105251904, 200711160, 383580180, 733704990

Offset: 0

Author

Ilya Gutkovskiy, Jan 29 2024

Keywords

• nonn

Crossrefs

Cf. A024939, A025591, A350457.

Programs

Maple

b:= proc(n) option remember; `if`(n<2, 1, expand(b(n-1)*(1+x^ithprime(n)))) end:
a:= n-> max(coeffs(b(n))):
seq(a(n), n=0..40);  # Alois P. Heinz, Jan 29 2024

Mathematica

Table[Max[CoefficientList[Product[(1 + x^Prime[k]), {k, 2, n}], x]], {n, 0, 40}]

PARI

a(n) = vecmax(Vec(prod(i=2, n, 1+x^prime(i)))); \\ Michel Marcus, Jan 29 2024

Python

from collections import Counter
from sympy import prime
def A369708(n):
    c = {0:1}
    for i in range(2,n+1):
        p, d = prime(i), Counter(c)
        for k in c:
            d[k+p] += c[k]
        c = d
    return max(c.values()) # Chai Wah Wu, Jan 31 2024